What is (\partial)/(\partial x)(ln(4+x^2y^2)) ?

The answer to (\partial)/(\partial x)(ln(4+x^2y^2)) is (2xy^2)/(4+x^2y^2)

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(\partial)/(\partial x)(ln(4+x^2y^2))

\frac{\partial}{\partial x} (ln (4 + x^{2} y^{2}))

\frac{2 x y ^{2}}{4 + x ^{2} y ^{2}}

Solution steps

\frac{\partial}{\partial x} (ln (4 + x^{2} y^{2}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{4 + x ^{2} y ^{2}} \frac{\partial}{\partial x} (4 + x^{2} y^{2})

= \frac{1}{4 + x ^{2} y ^{2}} \frac{\partial}{\partial x} (4 + x^{2} y^{2})

\frac{\partial}{\partial x} (4 + x^{2} y^{2}) = 2 y^{2} x

= \frac{1}{4 + x ^{2} y ^{2}} \cdot 2 y^{2} x

Simplify

\frac{1}{4 + x ^{2} y ^{2}} \cdot 2 y^{2} x : \frac{2 x y ^{2}}{4 + x ^{2} y ^{2}}

= \frac{2 x y ^{2}}{4 + x ^{2} y ^{2}}

(x^{2} + y^{2})^{2} = 4 x^{2} y, (1, 1)

\int \frac{- 12}{x ^{2} 4 - x ^{2}} d x

\frac{\partial}{\partial x} (4 x^{2} + y^{2} - 7 y)

\frac{d}{d x} (\frac{6 x}{x ^{2} + 3})

\frac{d}{d x} (\frac{1}{( x ^{3} + 9 ) ^{5}})

What is (\partial)/(\partial x)(ln(4+x^2y^2)) ?
The answer to (\partial)/(\partial x)(ln(4+x^2y^2)) is (2xy^2)/(4+x^2y^2)